Because the fabrication of prototype integrated circuit designs is expensive and time consuming, it is typical for circuit designers to first simulate their designs using computer simulation tools. In this way corrections can be made before the time and expense of prototype fabrication is incurred. One popular family of circuit simulators, especially useful for analog performance verification and behavior prediction, is known generically as SPICE (Simulation Program with Integrated Circuits Emphasis). The family includes the original SPICE program, numerous subsequent versions of the program, and numerous offshoots available from other sources. Circuit simulators are used often for predicting and verifying, among other things, the steady state analog behavior of a circuit, the transient analog behavior of a circuit, and the RF behavior of a circuit.
Generally, analog circuit simulators operate by describing the circuit in terms of nodes and devices. Each terminal of a device constitutes a node of the circuit. Different nodes can be connected together. Each device is described by a device “model”, which either formulaically or algorithmically defines performance measures such as the current/voltage relationships that the device imposes on its terminals. Often a number of different models are available for use in describing a particular kind of device. For example, a large number of models are available to describe a Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET), some designed for fast computation and others designed for better accuracy and for taking into account particular semiconductor effects. Typically the models require the user to specify values for a number of global parameters that apply to all transistors represented by the model, and optionally also allow the user to specify values for a number of instance parameters that are to apply to only one particular transistor instance. Some models are based on parameter values to be entered explicitly by the user, such as VTO and ION, but most are based on transistor layout characteristics such as channel length and width.
It has long been known that semiconductor materials such as silicon and germanium exhibit the piezoresistive effect (mechanical stress-induced changes in electrical resistance). See for example C. S. Smith, “Piezoresistance effect in germanium and silicon”, Phys. Rev., vol. 94, pp. 42-49 (1954), incorporated by reference herein. The piezoresistive effect has formed the basis for certain kinds of pressure sensors and strain gauges, but only recently has it received attention in the manufacture of integrated circuits. In integrated circuit fabrication, one of the major sources of mechanical stress is the differential expansion and contraction of the different materials used. For example, typical fabrication technologies involve electrically isolating the active regions of groups of one or more transistor by surrounding them with shallow trench isolation (STI) regions which are etched into the silicon and then filled with an insulator, such as an oxide. During cooling, oxides tend to shrink less than the surrounding silicon, and therefore develop a state of compressive stress laterally on the silicon regions of the device. Of significance is the stress exerted by the STI regions on the silicon forming a MOSFET channel, because the piezoresistive impact of such stress can affect carrier mobility, and therefore both current flow through the channel (Ion) and transistor switching speed.
The stress exerted on a region of silicon decays rapidly as a function of distance from the stress-causing interfaces. In the past, therefore, while process technologies could not produce today's extremely narrow channel widths, the stress-induced impact on performance could be ignored because only the edges of the diffusion region (adjacent to the STI regions) were affected. The channel regions were too far away from the STI regions to exhibit any significant effect. As process technologies have continued to shrink, however, the piezoresistive effect on transistor performance is no longer negligible.
Technology Computer Aided Design (TCAD) models are frequently used to model the behavior of integrated circuit devices at the level of individual transistors. Behaviors characterized at this level can be fed back to improve the circuit layout or the fabrication process, or they can be used to derive circuit level parameters (e.g. SPICE parameters) of the device for subsequent analysis of the circuit at macroscopic levels. TCAD analysis has long been able to take stress effects into account, but only by performing 3-dimensional finite element analysis of a single transistor or a small fragment of the chip. The computation time required to obtain accurate results, however, limited the utility of this kind of analysis to only small regions of a chip layout that include only several transistors. For example, it has not been practical to perform a TCAD analysis to obtain reasonably accurate circuit level parameters for layout regions larger than about a dozen transistors, or about 2-3 diffusion regions. Even then, huge amounts of CPU time, up to several hours per transistor, were required to obtain reasonably accurate results. Even as computing power increases, the required computation time continues to make this approach prohibitively expensive for any large fragments of the chip layout.
The simplified transistor models in SPICE are provided to drastically reduce the computing power necessary to simulate a circuit, for situations in which the accuracy of full finite element analysis is not critical. The simplified models are constantly undergoing improvement, the effort usually being to improve simulation accuracy while continuing to avoid a full finite element analysis. Recently, a simplified model was developed for taking into account stress effects on electron and hole mobilities. See R. A. Bianchi et al., “Accurate Modeling of Trench Isolation Induced Mechanical Stress Effects on MOSFET Electrical Performance,” IEEE IEDM Tech. Digest, pp. 117-120 (December 2002), and U.S. Patent Publication No. 2002/0173588 (2003), now U.S. Pat. No. 6,569,941, both incorporated herein by reference. A variation of this model, with some additional fitting terms and parameters, was incorporated into Revision 4.3.0 of the Berkeley BSIM standard model. See Xuemei (Jane) Xi, et al., “BSIM4.3.0 Model, Enhancements and Improvements Relative to BSIM4.2.1”, University of California at Berkeley (2003), available at http://www-device.eecs.berkeley.edu/˜bsim3/BSIM4/BSIM430/doc/BSIM430_Enhance ment.pdf, incorporated by reference herein. The model is known as the Length of Diffusion (LOD) model, since its primary parameter is the length of the diffusion region on each side of the channel of a transistor under study. Roughly, the user enters instance parameter values that describe the LOD at different segments along the width of the channel, and a procedure in the model calculates a weighted average LOD for the entire channel width. It then calculates a stress based on the weighted average LOD, and then converts that stress value to a change in mobility. The change in mobility is applied to the value of the global mobility parameter to develop the mobility that will be used for further calculations within the model. This mobility value is also itself available as an output of the model. The LOD method for approximating a carrier mobility adjustment has now been incorporated into certain SPICE models for describing a MOSFET device.
The LOD model is one example of what is referred to herein as a “simplified” model for evaluating stress effects on transistor performance. Any model that trades off accuracy in favor of computation speed, as compared to a full finite element analysis, is considered herein to be a “simplified” model. Other simplified models have been proposed as well, such as the model described in U.S. patent application Ser. No. 11/291,294, filed 1 Dec. 2005, entitled Analysis Of Stress Impact On Transistor Performance, incorporated by reference in its entirety herein, but these have not yet been incorporated into standardized SPICE device models.
Unfortunately, the LOD model has a number of deficiencies. First, the model is limited to STI-induced stress. It therefore ignores many other potential sources of stress. For example, some integrated circuit manufacturers form SiGe in the source and drain areas of a p-channel transistor intentionally to induce certain stresses on the channel; this source of stress is not taken into account in the LOD model, nor are stresses induced by differential coefficients of expansion of superposing layers. Additionally, several semiconductor manufacturers use strained cap layers covering the transistors on top of the gate stacks. It is typical to use tensile nitride cap layers for n-channel transistors and compressive nitride cap layers for p-channel transistors. Some other potential stress sources include tensile STI that is beneficial for both n-channel and p-channel transistors and tensile Si:C (carbon-doped silicon) in the source/drain of the n-channel transistors. None of these stress sources are taken into account by the LOD methodology.
Second, the LOD model fails to take into account stresses that might be present transversely to the length of diffusion, across the channel width-wise. It has been discovered that compressive stress in this direction can affect carrier mobility in the channel in significant and surprising ways.
Third, more generally than the second deficiency, since the LOD model considers only hydrostatic pressure, which is a sum of all normal (i.e. volume changing rather than rotational) stress components, it fails to take into account differing vector stress components. Different stress components relative to the channel direction are known to affect carrier mobility differently.
Fourth, the LOD model fails to take into account the presence of other structures in the neighborhood of a region under study, apart from the nearest STI interface. Other structures beyond this interface might reduce the amount of oxide presumed to be exerting a force, and therefore might reduce the actual stress in the channel.
Accordingly, it would be extremely desirable to provide a way of adjusting standard SPICE device models to account for the stress impact on transistor characteristics, more accurately than does the LOD model.
Roughly described, this can be accomplished by first selecting a first transistor performance measure that is affected by stress in the transistor channel, and then using a first, stress-sensitive, transistor model to develop a mathematical relationship between the first transistor performance measure and one or more instance parameters that are available as inputs to a second, stress-insensitive, transistor model. The first transistor model is typically one that is not as accurate as desired, but is acceptably accurate for certain types of layout geometries. The second transistor model may for example be the same as the first model, with its stress sensitivity disabled. Once the mathematical relationship has been determined, any other stress analyzer can be used in substitution for the stress aspects of the first model. Specifically, the substitute stress analyzer can be used to determine a stress-adjusted value for the first performance measure, and the mathematical relationship is used to convert that value into specific values for the one or more instance parameters. These values are then provided to the second, stress-insensitive, transistor model for use in simulating the characteristics of the particular transistor during circuit simulation. In essence the instance parameter values (or variations in them) can be thought of as substituting for the stress analysis that the first transistor model would have applied.
Preferably the substitute stress analyzer is more accurate than the stress sensitive aspects of the first transistor model, or is more accurate for at least some layout conditions, or takes more different layout conditions into account than do the stress sensitive aspects of the first transistor model. In an example, the stress analysis performed by the first model is LOD-based, and the stress analysis performed by the substitute stress analyzer takes into account one or more of the stress sources or layout features not taken into account by the LOD model. In an example, the first performance measure is carrier mobility (electron mobility for N-channel devices, and hole mobility for P-channel devices).
In an embodiment, the substitute stress analyzer itself relies on calibration coefficients that must be determined empirically. In this embodiment, the calibration coefficients are determined such that the substitute stress analyzer generates the same values for the first transistor performance measure that would be generated by the first (stress-sensitive) transistor model, at least for a subset of layout geometries for which the first transistor model generates what are deemed to be relatively accurate values for the first performance measure.
In an embodiment, the mathematical relationship between the first transistor performance measure and the instance parameters is developed by using the first transistor model to simulate a plurality of test transistors to determine a value for a second performance measure for each test transistor. The second performance measure preferably (but not necessarily) is different from the first performance measure, and may for example be data representing a set of I-V curves for the particular test transistor. The second transistor model is then used to simulate the same plurality of test transistors to determine corresponding instance parameter values that, when applied in the second model, generate the same values for the second performance measure as were developed using the first transistor model. Each test transistor thus has associated therewith both a value for the first performance measure, as generated by the first transistor model, and a set of instance parameter values, that can be used in the second transistor model in substitution for the stress calculations of the first transistor model. The resulting correlation between particular sets of instance parameter values and corresponding first performance measure values either can be retained in tabular format, or can be fit to one or more mathematical functions. In either case, the desired mathematical relationship has been established.
The above mechanism thus enables a system to perform circuit simulation in a manner that is consistent with the first transistor model so far as it goes, but extended in a manner consistent with additional insights captured by the substitute model. Other uses for the above mechanism will also be apparent to the reader.